Infinite Linear Systems M/G/\(\infty\) and Multilinear Systems with M/G/n/0 Losses

The method based on the description of the probabilities of states using a non-stationary Poisson flow allows using elementary reasoning to find not only a stationary, but also a non-stationary distribution of the number of requirements in the system.

To find a stationary distribution of the number of requirements in queuing systems (QS), the method of introducing additional variables leading to a piecewise linear Markov process is used.

The fact of invariance is shown: the stationary probabilities of pi states in queuing systems (QS) M/G/n/0 depend only on the average service time of the requirement and do not depend on the type of distribution G(x).